t-extending Krasner hypermodules
DOI:
https://doi.org/10.5269/bspm.51589Abstract
Let M be a hypermodule over a hyperring R such that the intersection of any two subhypermodules of M is a subhypermodule of M. We introduce the concept of an t-essential subhypermodule in M relative to an arbitrary subhypermodule T of M, which is called T-t-essential subhypermodule of M. Our aim in this work is to investigate properties of t-essential subhypermodules. We apply this concept to introduce t-extending hypermodules. Examples are provided to illustrate different concepts.
References
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2. Anderson, F. W., Fuller, K. R., Rings and Categories of Modules, Springer-Verlag, New York (1992). https://doi.org/10.1007/978-1-4612-4418-9
3. Anvariyeh, S. M., Davvaz, B., Strongly transitive geometric spaces associated to hypermodules, Journal of Algebra 322, 1340-1359, (2009). https://doi.org/10.1016/j.jalgebra.2009.05.014
4. Asgari, S. H., Haghany, A., t-extending Modules and t-Baer Modules, Communications in Algebra 39, 1605-1623, (2011). https://doi.org/10.1080/00927871003677519
5. Corsini, P., Prolegomena of Hypergroup Theory, 2nd ed. Tricesimo Italy, Aviani editore Italy, (1993).
6. Davvaz, B., Remarks on weak hypermodules, Bull. Korean Math. Soc. 36(3), 599-608, (1999).
7. Davvaz, B., Fotea, V. L., Hyperring Theory and Applications, Palm Harbor, FL, USA International Academic Press, (2007).
8. Fotea, V. L., uzzy hypermodules, Computers and Mathematics with Applications 57, 466-475, (2009). https://doi.org/10.1016/j.camwa.2008.11.004
9. Hamzekolaee, A. R. M., Norouzi, M., A hyperstructural approach to essentially, Communications In Algebra 46(11), 4954-4964, (2018). https://doi.org/10.1080/00927872.2018.1459649
10. Krasner, M., A class of hyperrings and hyperfields, IJMMS 6(2), 307-311, (1999). https://doi.org/10.1155/S0161171283000265
11. Omidi, S., Davvaz, B., Hyperideal theory in ordered Krasner hyperrings, An. S¸t. Univ. Ovidius Constanta 27(1), 193-210, (2019). https://doi.org/10.2478/auom-2019-0010
12. Lam, T. Y., Lectures on Modules and Rings, Graduate Texts in Mathematics. 189, New York, Springer-Verlag, (1998). https://doi.org/10.1007/978-1-4612-0525-8
13. Wisbauer, R., Foundations of module and ring theory, Gordon and Breach, (1991).
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2022-02-04
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